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# Sum of n consecutive integers

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Posted 13 July 2013 - 02:25 AM

You may already know that 1+2+3+4+5=15. Let's try five other consecutive integers: 14+15+16+17+18=80. How about -1+0+1+2+3=5? We might guess that the sum of 5 consecutive integers is divisible by 5. That turns out to be true. Maybe the sum of n consecutive integers is divisible by n. That turns out not to be true: 1+2 is not divisible by 2.

Question: When is the sum of n consecutive integers divisible by n, and when is it not divisible by n?

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### #2 vistaptb

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Posted 13 July 2013 - 02:46 AM

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Posted 13 July 2013 - 03:15 AM

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this is correct but can you prove it?

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### #4 gavinksong

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Posted 13 July 2013 - 12:00 PM

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Posted 13 July 2013 - 05:43 PM   Best Answer

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Edited by BMAD, 13 July 2013 - 05:43 PM.

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